Canada and Mexico must maintain a united front in confronting U.S. President Donald Trump, Mexico's Economy Minister says, because they stand to gain more together than they might negotiating alone.

"You cannot fall into the temptation to get a specific privilege that will cost certainty and direction to the world," Ildefonso Guajardo told The Globe and Mail in an interview in his office in Mexico City. "NAFTA is trilateral and should be handled as a trilateral discussion … Regardless of the temptations in this process to go different ways, you can never go against principles. The first one is: Nothing that results in tariffs and quotas in trade – that would be a move to the past."

His words were echoed in recent days by several senior advisers to the administration of Mexican President Enrique Pena Nieto who are anxious to see Canada back Mexico in standing up to Mr. Trump's threat to "tear up" the North American free-trade agreement.

Of course Canada must defend its own interests, Mr. Guajardo said. "It's the same for Mexico: Our first responsibility is to look after our country's interest, and no one can contradict that. But … in doing that you do not need to run over other nations with your bus. You can do both things."

The United States is by far the largest trading partner of both Mexico and Canada. In 2015, Mexico and Canada each exported about $295-billion (U.S.) in goods to the United States. But the U.S. goods-trade deficit with Mexico was much larger – about $58-billion – so Mexico has become the focus of Mr. Trump's criticism of U.S. trade policy; he has said that trade terms with Canada require only "tweaking." But the Mexicans are hoping Canada stands by them.

Mr. Guajardo also made explicit the threat that Mexico will bring to any trade negotiations with the United States: an end to co-operation with the U.S. government on drugs, migration and intelligence.

"There is so much at stake for the interest of the U.S. as a country," he said. "We have been a great ally to fight problems with migration, narcotics … If at some point in time things become so badly managed in the relationship, the incentives for the Mexican people to keep on co-operating in things that are at the heart of [U.S.] national-security issues will be diminished. You cannot ask me to [accept poor] conditions in terms of trade and then request my help to manage migration issues from other nations or … the prosecution of criminal activities and narcotics."

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Prime Minister Justin Trudeau called Mr. Pena Nieto shortly after meeting with Mr. Trump in Washington on Feb. 13, their third phone conversation in three weeks.

"Since we were not able to have our President going to Washington, I would imagine that President Pena would love to know what happened and what kinds of discussions they had internally about NAFTA and the bilateral and trilateral relationships," said Jaime Zabludovsky, who was Mexico's deputy negotiator on NAFTA and now advises the Mexican President.

Mr. Pena Nieto cancelled a trip of his own to meet Mr. Trump after the U.S. President insisted via Twitter that he must come prepared to pay for a planned wall on the U.S.-Mexican border.

The Canadian government has been reiterating the value of its relationship with Mexico while avoiding any commitment to a purely trilateral discussion of NAFTA.

"Mexico is our friend," Trade Minister François-Philippe Champagne told reporters in Berlin on Thursday. "We'll see how the process is going with respect to NAFTA … We'll let them do their process with the United States, but we've been clear to them that the Mexicans are our friends and we'll always be willing to talk to them because trade has been beneficial … Certainly we'll let them do their process with the U.S., but we'll always be there for a friend to look at what we can achieve together following their own process with the U.S."

There is intense frustration among those advising President Pena Nieto that Mr. Trump and his closest advisers seem to have a limited understanding of how international trade works and focus obsessively on the trade deficit with Mexico without acknowledging that it is just 8 per cent of the overall U.S. trade deficit and far below its trade deficit with China. "They are obsessed by the trade deficit – that is the only indicator that they use," Mr. Zabludovsky said.

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The focus now, said one senior Mexican trade negotiator, is to find "a fig leaf that is big enough to give these guys" – that is, offer Mr. Trump a way to avoid embarrassment and tell his supporters he successfully renegotiated NAFTA while actually improving the deal for all parties.

Mexico's broader strategy is to let the process unfold as slowly as possible, allowing time for Mr. Trump's advisers to understand the degree to which North American supply chains are integrated and how difficult it would be to break them up; for the pro-trade lobby in Congress to organize; and for representatives of the states that rely heavily on agricultural exports to Mexico to make their case that NAFTA must be preserved.

Luis de la Calle, a former NAFTA negotiator who now advises the government, said the threat of losing Mexico as a market for pork, corn and poultry is a significant one.

"The key to a successful negotiation strategy with the U.S. is not to have a strategy to diversify your exports but a strategy to diversify your imports. This is counterintuitive, but the driver for U.S. lobbying efforts to convince the Trump administration and the Congress that Mexico is important to them is if they know we have suppliers outside the U.S. for the very large Mexican market. Mexico is going to be the largest market for the U.S. in five years – larger than Canada and larger than the EU," Mr. de la Calle said.

Canada and Australia will be held up as the potential replacements, because they have already negotiated terms and because they are "an easy substitute for the U.S. Midwest."

Mr. Guajardo said Canada and Mexico need to retain NAFTA regardless of what the United States opts to do. "NAFTA is not all about trade rules. It's about rules that give certainty to investors. And sending the message that the instrument is alive, and will continue, is of extreme value to world investors to come to Mexico and probably to Canada."

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Mr. Zabludovsky, who was also the lead negotiator on Mexico's free-trade pact with Europe, said Canada and Mexico now have a global opportunity and obligation to fill a leadership vacuum in the absence of the United States. "Hopefully, Mexico and Canada are able to really play that role that the U.S. is not willing to play any more." He cited the regional integration of the Americas under way and the now-scrapped Trans-Pacific Partnership.

"If Mexico and Canada are able to start with NAFTA and show that we are willing to work together and defend and protect and hopefully enhance and improve NAFTA, then we will be in a position to talk to the rest of the world as two countries that are really committed to integration … To some extent nobody can substitute for the U.S., but if the U.S. is not willing to play that role, I think that there will be the need for countries like Mexico and Canada."

With files from Bill Curry

Video: While Trudeau and Trump praise Canada-U.S. trade agreements, the president adds ‘we’ll be tweaking it’

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